The conclusion was that you don’t get interference regardless of what you do at the other end, because the paths are potentially distinguishable. There would only be interference when paths are indistinguishable. In other words, photons in the entangled state are kind of weird. I think in terms of the discussion above, you might say that such a photon needs to be described by a density matrix rather than a state vector. This makes it work a little differently than photons from simpler sources.
That is a good puzzle, Jeff. I remember debating a similar experiment a few years ago on a mailing list. At the time I discovered an analysis of a related idea at http://www.flownet.com/gat/QM.pdf.
The conclusion was that you don’t get interference regardless of what you do at the other end, because the paths are potentially distinguishable. There would only be interference when paths are indistinguishable. In other words, photons in the entangled state are kind of weird. I think in terms of the discussion above, you might say that such a photon needs to be described by a density matrix rather than a state vector. This makes it work a little differently than photons from simpler sources.